David Cameron warns on Monday that the eurozone risks facing perpetual economic stagnation from an unresolved crisis or a breakup caused by a failure to address its underlying economic failures.

Britain will feel the impact of any continuing crisis, the prime minister will say in a speech at the G20 summit of the world's leading economies which starts in Mexico today. The summit will last two days.

Cameron will urge the political classes in Europe to recognise how incredibly high the stakes have become and he will plead for a decisive response from them.

He is also expected to assess the state of the euro economy after the Greek elections as he lands in Mexico with his chancellor, George Osborne. There they will meet other world leaders as they gather in the Mexican coastal resort of Los Cabos. Cameron will be updated on the state of the world's stock markets and the eurozone's reaction to the Greek elections as he flies to Mexico.

In a speech to business leaders in Los Cabos before the summit opens, Cameron will argue for European partners to come to a decision and not to delay any longer. That suggests he is desperate to see a resolution of the Greek crisis one way or another, rather than further lengthy negotiations about changing the terms of the country's bailout package. He will also argue against solving the sovereign debt crisis with extra borrowing.

Directly urging his eurozone partners to get a grip, he will say: "The reality is that there are a set of things the eurozone countries need to do, and it is up to the eurozone countries to decide whether they are prepared to make the sacrifices these entail. The challenge is as much of political will as of economics. Of course these things are difficult to do, but just because things are difficult does not mean we should not say them.

"If the eurozone is to stay together, then it has to make at least some of these difficult decisions. The alternatives to action that create a more coherent eurozone are either perpetual stagnation from a eurozone crisis that is never resolved or a breakup caused by a failure to address underlying economic fundamentals that would have financial consequences that would damage the world economy – including Britain".

At the same time, Cameron will urge the European Central Bank to take more measures to stimulate growth through forms of credit easing and guaranteed loans, similar to the measures announced by the Bank of England on Thursday.

In remarks that clash with the anti-austerity thinking advanced by the French President François Hollande and the US President Barack Obama, Cameron will insist the solution to low economic growth lies in monetary activism and structural reform, as opposed to stimulating demand.

He will say: "If a country wants growth in its national economy, then it has to deal with its debts, and dealing with its debts is every bit as essential as for the global economy. Countries simply cannot continue to run indefinite structural fiscal deficits without contributing to the fundamental imbalances that fuelled the 2008 crisis.

"The world is gripped by five inter-related threats: the eurozone crisis, sovereign debt, the challenges of growth and low competitiveness, protectionism and failure to regulate the banking system."

Cameron will also call on world leaders to take more action on the commitments made at previous summits on a new global financial architecture. The prime minister will argue: "This demands courage, resolve, political commitment", adding "it is easy to sign up to declarations, but much harder to push through the difficult changes that are vital to generate the growth and the jobs that our citizens demand".

He will point out that six G20 countries have yet to start to implement international rules requiring banks to hold bigger cushions of capital, and he will call for tougher monitoring of progress on this.

Britain is concerned by signs of self-defeating protectionism as world trade conditions worsen. He will point to 124 acts of trade restrictions in the last eight months. But he will argue that China and the US have taken action to reduce global trade imbalances – the Chinese by an appreciation of their exchange rate and the Americans by reducing their current deficit from 5% to 3%. Nevertheless, he will say more needs to be done.

Cameron's comments on the continuing fragility in the eurozone followed a warning by Labour's former prime minster Tony Blair who called on Germany to use its financial might to shore up the euro. Blair said the Germans would do this only if wide-ranging reforms were delivered by European governments.

Lord Mandelson warned that Greece "faces a very long and very painful road back" and urged leaders to take action.